Currently, the most stringent bound on the spin-independent DM-nucleon cross section is provided by the LUX experiment [1]}, with the minimum cross section of \(7.6\times 10^{-46}~{\rm cm}^2\)  for a DM mass of 33 GeV. It is shown in Fig. REF  that the LUX experiment has already probed some parameter space required by the DM relic abundance. Especially, the low DM mass region with \(M_H \leqslant 52\)  GeV is actually ruled out, as indicated by the shaded area in the plot. However, most parameter spaces are still allowed by LUX.
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